Systems and methods to identify open phases of a capacitor bank

ABSTRACT

Methods and devices are provided for determining the number of open phases and which particular phases may be open in capacitor bank system. Detecting open phases may include determining a neutral current of the capacitor bank system. According to one detection method, in response to a magnitude of the neutral current being greater than a threshold value, an IED may calculate an aggregate power phasor for the phases of the capacitor bank system with respect to each rotation. According to another detection method, in response to the magnitude of the neutral current being greater than a threshold value, an IED may calculate an individual power phasor for each of the phases of the capacitor bank system with respect to each rotation. Based on the magnitude and angles of the power phases, the IED may determine the presence of open phases and which particular phases may be open, respectively.

BACKGROUND

This disclosure relates to monitoring an electric power distributionsystem. More particularly, this disclosure relates to determiningoperating conditions of capacitor bank phases within the electric powerdistribution system.

This section is intended to introduce the reader to various aspects ofart that may be related to various aspects of the present techniques,which are described and/or claimed below. This discussion is believed tobe helpful in providing the reader with background information tofacilitate a better understanding of the various aspects of the presentdisclosure. Accordingly, it should be understood that these statementsare to be read in this light, and not as admissions of any kind.

Electric power distribution systems carry electricity from atransmission system to residential communities, factories, industrialareas, and other electricity consumers. Within an electric powerdistribution system, a capacitor bank may include multiple capacitorsand store electrical charge. The capacitors within the capacitor bankmay be configured as a multi-phase system (e.g., three-phase system).Capacitor banks help maintain bus voltage and power factor of theelectric power distribution system within acceptable limits, and thusreduce electrical transmission line losses. However, blown fuses, switchfailures, jumper failures, capacitor failures, and so forth may resultin one or more open phases of the capacitor bank, thereby causingoperational issues within the electric power distribution system.

SUMMARY

Certain examples commensurate in scope with the originally claimedsubject matter are discussed below. These examples are not intended tolimit the scope of the disclosure. Indeed, the present disclosure mayencompass a variety of forms that may be similar to or different fromthe examples set forth below.

In one example, a method for determining which phases of a multi-phasecapacitor bank system are open is provided. A neutral current of themulti-phase capacitor bank system may be calculated. Based on amagnitude of the neutral current being greater than a first thresholdvalue, a power phasor with respect to an ABC rotation, an ACB rotation,or both of the multi-phase capacitor bank system may be calculated. If amagnitude of the power phasor is greater than a second threshold value,then one or more phases may be open within the multi-phase capacitorbank system. After determining that one or more phases are open, a phaseangle of the power phasor may be used to determine which of the one ormore phases are open and a notification indicating the one or morephases that are open may be issued.

In another example, tangible, non-transitory, computer-readable mediamay include instructions that, when executed by a processor of anintelligent electronic device that controls at least part of anelectrical distribution system, cause the processor to determine aneutral current of a multi-phase capacitor bank system. In response to amagnitude of the neutral current being greater than a first thresholdvalue, the processor may calculate a power phasor for each phase themulti-phase capacitor bank system with respect to an ABC phase rotation,an ACB phase rotation, or both. The processor may determine that one ormore phases are open within the multi-phase capacitor bank system inresponse to each magnitude of each power phasor being greater than asecond threshold value. Further, the processor may determine which ofthe one or more phases are open based on each phase angle of each powerphasor and issue a notification indicating the one or more phases thatare open.

In another example, an intelligent electronic device includes processingcircuitry, a communication system, and a memory device. The memorydevice includes instructions that cause the processing circuity tocalculate a power phasor for each phase of a multi-phase capacitor banksystem with respect to an ABC phase rotation, an ACB phase rotation, orboth. In response to each magnitude of each power phasor being greaterthan a threshold value, the processing circuitry may determine which ofthe one or more phases are open based on each phase angle of each powerphasor and issue a notification indicating the one or more phases thatare open.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified diagram of an electric power distribution system,in accordance with an embodiment;

FIG. 2 is a block diagram of a three-phase capacitor bank system of theelectric power distribution system of FIG. 1 , in accordance with anembodiment;

FIG. 3 is a flowchart of a process used to determine open phases of thethree-phase capacitor bank system of FIG. 2 by computing a single phasorbased on voltages of the three phases, in accordance with an embodiment;

FIG. 4 is a schematic diagram of an ABC rotation used to identify openphase(s) based on a phase angle of the single phasor of FIG. 3 , inaccordance with an embodiment;

FIG. 5 is a schematic diagram of an ACB rotation used to identify openphase(s) based on a phase angle of the single phasor of FIG. 3 , inaccordance with an embodiment;

FIG. 6 is a flowchart of another process used to determine open phasesof the three-phase capacitor bank system of FIG. 2 by computing threedifferent power phasors for each voltage of the three phases, inaccordance with an embodiment;

FIG. 7 is a schematic diagram of an ABC rotation used to identify anopen phase based on each phase angle of the three different powerphasors of FIG. 6 , in accordance with an embodiment;

FIG. 8 is a schematic diagram of an ABC rotation used to identify twoopen phases based on each phase angle of the three different powerphasors of FIG. 6 , in accordance with an embodiment;

FIG. 9 is a schematic diagram of an ACB rotation used to identify anopen phase based on each phase angle of the three different powerphasors of FIG. 6 , in accordance with an embodiment; and

FIG. 10 is a schematic diagram of an ACB rotation used to identify twoopen phases based on each phase angle of the three different powerphasors of FIG. 6 , in accordance with an embodiment.

DETAILED DESCRIPTION

One or more specific embodiments will be described below. In an effortto provide a concise description of these embodiments, not all featuresof an actual implementation are described in the specification. Itshould be appreciated that in the development of any such actualimplementation, as in any engineering or design project, numerousimplementation-specific decisions must be made to achieve thedevelopers' specific goals, such as compliance with system-related andbusiness-related constraints, which may vary from one implementation toanother. Moreover, it should be appreciated that such a developmenteffort might be complex and time consuming, but would nevertheless be aroutine undertaking of design, fabrication, and manufacture for those ofordinary skill having the benefit of this disclosure. Certain examplescommensurate in scope with the originally claimed subject matter arediscussed below. These examples are not intended to limit the scope ofthe disclosure. Indeed, the present disclosure may encompass a varietyof forms that may be similar to or different from the examples set forthbelow.

When introducing elements of various embodiments of the presentdisclosure, the articles “a,” “an,” and “the” are intended to mean thatthere are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.Additionally, it should be understood that references to “oneembodiment” or “an embodiment” of the present disclosure are notintended to be interpreted as excluding the existence of additionalembodiments that also incorporate the recited features. Furthermore, thephrase A “based on” B is intended to mean that A is at least partiallybased on B. Moreover, unless expressly stated otherwise, the term “or”is intended to be inclusive (e.g., logical OR) and not exclusive (e.g.,logical XOR). In other words, the phrase “A or B” is intended to mean A,B, or both A and B.

Moreover, the embodiments of the disclosure will be best understood byreference to the drawings, wherein like parts are designated by likenumerals throughout. The components of the disclosed embodiments, asgenerally described and illustrated in the figures herein, could bearranged and designed in a wide variety of different configurations.Thus, the following detailed description of the embodiments of thesystems and methods of the disclosure is not intended to limit the scopeof the disclosure, as claimed, but is merely representative of possibleembodiments of the disclosure. In addition, the steps of a method do notnecessarily need to be executed in any specific order, or evensequentially, nor need the steps be executed only once, unless otherwisespecified. In some cases, well-known features, structures or operationsare not shown or described in detail. Furthermore, the describedfeatures, structures, or operations may be combined in any suitablemanner in one or more embodiments. The components of the embodiments asgenerally described and illustrated in the figures could be arranged anddesigned in a wide variety of different configurations.

In addition, several aspects of the embodiments described may beimplemented as software modules or components. As used herein, asoftware module or component may include any type of computerinstruction or computer-executable code located within a memory deviceand/or transmitted as electronic signals over a system bus or wired orwireless network. A software module or component may, for instance,include physical or logical blocks of computer instructions, which maybe organized as a routine, program, object, component, data structure,or the like, and which performs a task or implements a particular datatype.

In certain embodiments, a particular software module or component mayinclude disparate instructions stored in different locations of a memorydevice, which together implement the described functionality of themodule. Indeed, a module or component may include a single instructionor many instructions, and may be distributed over several different codesegments, among different programs, and across several memory devices.Some embodiments may be practiced in a distributed computing environmentwhere tasks are performed by a remote processing device linked through acommunications network. In a distributed computing environment, softwaremodules or components may be located in local and/or remote memorystorage devices. In addition, data being tied or rendered together in adatabase record may be resident in the same memory device, or acrossseveral memory devices, and may be linked together in fields of a recordin a database across a network.

Thus, embodiments may be provided as a computer program productincluding a tangible, non-transitory, computer-readable and/ormachine-readable medium having stored thereon instructions that may beused to program a computer (or other electronic device) to performprocesses described herein. For example, a non-transitorycomputer-readable medium may store instructions that, when executed by aprocessor of a computer system, cause the processor to perform certainmethods disclosed herein. The non-transitory computer-readable mediummay include, but is not limited to, hard drives, floppy diskettes,optical disks, compact disc read-only memories (CD-ROMs), digitalversatile disc read-only memories (DVD-ROMs), read-only memories (ROMs),random access memories (RAMs), erasable programmable read-only memories(EPROMs), electrically erasable programmable read-only memories(EEPROMs), magnetic or optical cards, solid-state memory devices, orother types of machine-readable media suitable for storing electronicand/or processor executable instructions.

Intelligent electronic devices (IEDs) may be used to control certaindevices on an electric power distribution system. In examples discussedbelow, an IED may be a capacitor bank controller that controls acapacitor bank on the electric power distribution system. However, itshould be appreciated that the systems and methods of this disclosuremay employ any suitable IED to control any suitable device to control anaspect of an electric power distribution system. Thus, where thedisclosure below refers to a capacitor bank controller that uses thesystems and methods of this disclosure, this should be understood toencompass any other suitable IEDs to control any other suitable devicesfor an electric power distribution system. Likewise, where thedisclosure refers to wireless current sensors (WCSs) that may providecurrent measurements, this should be understood to encompass any othersuitable electrical measurement devices that transmit electricalmeasurements.

One type of electrical measurement device is a current sensor. A currentsensor may be used to reduce higher-voltage currents to lower values,enabling measurements of the electrical current flowing throughtransmission lines. Current sensors may provide these measurements toIEDs for applications such as protective relaying, electrical loadsurveying, verification of circuit energization, cost allocation,capacitor bank control, and demand alarming. Some wireless currentsensors may operate using energy harvested from a transmission line,allowing them to operate without separate electrical wiring to a powersource and/or without a battery or using a relatively smaller battery.

Some IEDs may receive electrical measurements from several wirelesselectrical measurement devices measuring different respective phases ofelectric power. For example, three-phase electric power may betransmitted by three respective transmission lines. Three-phase powergenerally involves three alternating-current (AC) electrical waveformsthat are offset from one another in phase by about 120°. The three-phasepower waveforms are generally similar to one another, though there maybe some variation in magnitude or harmonics from phase to phase. CertainIEDs, such as a capacitor bank controller, may control an electricalcomponent of the power distribution system, such as a capacitor bank,based on the present state of all three phases of power. The capacitorbank may include three different capacitors of three respective phasesA, B, and C. Each of the three different capacitors may be coupled tothree corresponding switches and fuses.

This disclosure describes systems and methods to identify the operatingcondition (e.g., open or close) of the three respective phases A, B, andC of the capacitor bank. In general, open phase conditions (e.g., oneopen phase, two open phases) result in failures within the electricdistribution power system such as a capacitor bank system. When thecircuit through the capacitor on any phase is closed, electrical currentcan be expected to flow through the capacitor on that phase. When anycomponent of the circuit through the capacitor is open, there will be noelectrical current flowing through the capacitor. Any electrical phaseof the capacitor bank system may fail in variety of way such as but notlimited to capacitor failures, jumper failures, switch failures, blownfuses, and fuse failures, and thereby resulting in open phaseconditions. For example, an open phase condition via a capacitor failuremay occur when a capacitor of the capacitor bank has been disconnectedfrom a respective transmission line of the capacitor bank system,experiences mechanical and/or electrical damage, and the like. Further,an open phase condition may occur when a fuse coupled to the capacitoris blown. As used herein, a fuse may be an electrical safety device thatremoves electrical current from an electrical circuit when the currentin the electrical circuit is higher than a threshold current. However,when a fuse is blown, the capacitor becomes an open circuit andelectrical current may no longer flow. Additionally, switch failures(e.g., switches that fail to close) may also lead to open phaseconditions with the capacitor bank system.

Voltage and current levels that are greater than a maximum operatingthreshold due to power surges and lightning strikes may lead to blownfuses, damage to capacitors, and/or switch failures, and therebyresulting in open phase conditions within the capacitor bank system.When one or more open phase conditions are present in the capacitor banksystem, the capacitor bank system may not be operational. As such, itmay be useful to alert maintenance personnel regarding open phases orfailures within the capacitor bank system so blown fuses, failedswitches, and damaged capacitors may be replaced with functionalelectrical equipment. In order to detect open phases within thecapacitor bank system, a neutral current of the capacitor bank systemmay be measured. A current sensor such as a neutral current sensor maymeasure the neutral current of the capacitor bank system. In someembodiments, the neutral current sensor may be coupled to the capacitorbank system via a wire. In other embodiments, the neutral current sensormay be a wireless current sensor (WCS). As used herein, the neutralcurrent is the vector sum of each of the phase currents (e.g., {rightarrow over (I_(CA))}, {right arrow over (I_(CB))}, {right arrow over(I_(CC))}) going through the capacitor bank system as later discussed inFIG. 2 . If the neural current is not zero, the neutral current mayrepresent the imbalance of phase currents within an unbalanced capacitorbank system. However, if the phase currents are balanced in terms ofmagnitude and angle within the capacitor bank system, the neutralcurrent may be zero.

The neutral current measurement may be transmitted to an IED (e.g.,capacitor bank controller). The IED may determine whether the neutralcurrent is greater than a threshold current. If the neutral current isgreater than the threshold current, then the IED may alert maintenancepersonal regarding open phases within the capacitor bank system. Whilethe IED may be able to determine the presence of open phases within thecapacitor bank system based on the neutral current measurement,unfortunately, the IED may not be capable of determining the number ofphases that are open and which particular phases are open. Further, theIED or maintenance personnel may inadvertently determine that thepresence of open phases may be due to an unbalanced capacitor banksystem or high harmonic content (e.g., from inverter-based energysources) rather than the capacitor bank failures discussed above.

Therefore, identifying the number of open phases and which particularphases may be open within a capacitor bank system may be useful inresolving any failures and maintaining an operational capacitor banksystem. Further, a recorded history of when each phase first became openmay be useful in updates to electrical system planning models. In oneembodiment, after analyzing the neutral current, the IED may calculate apower phasor for a single-phase capacitor bank system or a power phasorfor each rotation of a multi-phase capacitor bank system. By way ofexample, the IED may calculate a fundamental frequency (e.g., 50 Hz, 60Hz) of the neutral current so that the effect of the harmonic content inthe capacitor bank system may be eliminated. The IED may receive thefundamental frequency of the neutral current, which is the sum of theelectrical current of each phase (e.g., A, B, C) of the capacitor banksystem, from the neutral current sensor. If the magnitude of the neutralcurrent is less than a first threshold, the IED may determine that allthree phases are open or closed. If the magnitude of the neutral currentis greater than a second threshold current, then the IED may determinethe presence of one or two open phases within the capacitor bank system.In turn, to determine the number of open phases and which particularphases may be open, the IED may compute a power phasor for asingle-phase voltage installation or for each rotation of a multi-phasevoltage installation (e.g., three-phase voltage installation) withrespect to the capacitor bank system.

In a capacitor bank installation, voltage measurements may be taken froma single phase or from all three phases. In a single-phase voltageinstallation, the measured phase may be assumed to be VA, while VB andVC may either be measured as 0V, or may be replicated from VA. Whenreplicated from VA, VB and VC magnitudes are assumed to match that ofVA, and their angles are assumed to be at −120 and 120 degrees withrespect to VA for an ABC system rotation, or at 120 and −120 degreeswith respect to VA for an ACB system rotation. This is known as phantomvoltage.

In a single-phase voltage installation, the power phasor ({right arrowover (P_(ND))}) may be calculated by taking the product of a voltage({right arrow over (V₁)}) at the single phase and the fundamentalfrequency of the neutral current ({right arrow over (I_(N))}) as shownin the following formulas and assumptions:{right arrow over (P _(ND))}={right arrow over (V ₁)}*{right arrow over(I _(N))}  [1]{right arrow over (V ₁)}={right arrow over (V _(A))}+{right arrow over(a)}{right arrow over (V _(B))}+{right arrow over (a)}²{right arrow over(V _(C))}  [2]{right arrow over (a)}=1

120  [3]V ₁ =V _(A) ;V _(B) =V _(C)=0  [4]By way of example the voltage at the single phase may be the voltage atphase A given that the voltage at phase B and the voltage at phase C arezero or phantom voltages.

In one embodiment with respect to a three-phase voltage installation,the power phasor ({right arrow over (P_(ND))}) may be calculated basedon summing a vector product of the three voltages (e.g., {right arrowover (V_(A))}, {right arrow over (V_(B))}, {right arrow over (V_(C))})at each of the three phases A, B, and C and the fundamental frequency ofthe neutral current (e.g., |I_(N)|) as shown in equations [1] and [2]previously. The neutral current (e.g., |{right arrow over (I_(N))}|) forthe three-phase installation is based on the sum of the electricalcurrent at each of the three phases (e.g., {right arrow over (I_(CA))},{right arrow over (I_(CB))}, {right arrow over (I_(CC))}). Rotations ofthe three-phase voltage installation may include an ABC rotation or anACB rotation. In some embodiments, a voltage installation may includeany suitable number of phases and may be associated with more phaserotations than the ABC and ACB rotations or fewer phase rotations thanthe ABC or ACB rotations. After calculating the power phasor for eachrotation, the IED may determine whether the magnitude of the powerphasor is greater than a threshold value. If the magnitude of the powerphasor is greater than the threshold value, the IED may determine thepresence of open phases in the capacitor bank system. With respect toeach rotation, the IED may determine the number of open phases and whichparticular phases may be open based on the angle of the power phasor.

In another embodiment, with respect to a three-phase voltageinstallation, the IED may calculate three different power phasors (e.g.,{right arrow over (P_(NA))}, {right arrow over (P_(NB))}, {right arrowover (P_(NC))}) corresponding to the respective phases A,B, and C ateach rotation (e.g., ABC rotation, ACB rotation). The power phasor at asingle phase (e.g., phase A) is the vector product of the voltage (e.g.,V_(A)) at the single phase and the fundamental frequency of the neutralcurrent (e.g, {right arrow over (I_(N))}). After calculating the threedifferent power phasors for each rotation, the IED may determine whethereach of the magnitude of the three power phasor is greater than anotherthreshold value. If the magnitudes of each of the three power phasors isgreater than the other threshold value, then the IED may determine thepresence of open phases in the capacitor bank system. With respect toeach rotation, the IED may determine the number of open phases and whichparticular phases may be open based on the angle of each of the threepower phasors. It can be appreciated that a range of specific angles maybe identified to determine the number of open phases and whichparticular phases may be open. In additional and/or alternativeembodiments, differences between angle ranges may be used to determinethe number of open phases and which particular phases may be open.

FIG. 1 illustrates a simplified diagram of an electric powerdistribution system 100 (e.g., capacitor bank system) that may usechanges in wireless communication rates to determine whether to operatean IED using measurements from a wireless electrical measurement device.The electric power distribution system 100 may generate, transmit,and/or distribute electric energy to loads. As illustrated, the electricpower distribution system 100 includes electric generators 110, 112,114, and 116. The electric power distribution system 100 may alsoinclude power transformers 117, 120, 122, 130, 142, 144, and 150.Furthermore, the electric power delivery system may include lines 124,134, 136, and 158 to transmit and/or deliver power, circuit breakers152, 160, and 176 to control flow of power in the electric powerdistribution system 100, busses 118, 126, 132, and 148, and/or loads 138and 140 to receive the power in and/or from the electric powerdistribution system 100. A variety of other types of equipment may alsobe included in electric power distribution system 100, such as currentsensors (e.g., wireless current sensor (WCS) 184), potentialtransformers (e.g., potential transformer 182), voltage regulators,capacitors (e.g., capacitor 174) and/or capacitor banks (e.g., capacitorbank (CB) 188), antennas (e.g., antenna 186), and suitable other typesof equipment useful in power generation, transmission, and/ordistribution.

A substation 119 may include the electric generator 114, which may be adistributed generator, and which may be connected to the bus 126 throughthe power transformer 117 (e.g., step-up transformer). The bus 126 maybe connected to a distribution bus 132 via the power transformer 130(e.g., step-down transformer). Various distribution lines 136 and 134may be connected to the distribution bus 132. The distribution line 136may lead to a substation 141 where the distribution line 136 ismonitored and/or controlled using an IED 106, which may selectively openand close circuit breaker 152. A load 140 may be fed from distributionline 136. The power transformer 144 (e.g., step-down transformer), incommunication with the distribution bus 132 via distribution line 136,may be used to step down a voltage for consumption by the load 140.

A distribution line 134 may deliver electric power to a bus 148 of thesubstation 151. The bus 148 may also receive electric power from adistributed generator 116 via transformer 150. The distribution line 158may deliver electric power from the bus 148 to a load 138, and mayinclude the power transformer 142 (e.g., step-down transformer). Acircuit breaker 160 may be used to selectively connect the bus 148 tothe distribution line 134. The IED 108 may be used to monitor and/orcontrol the circuit breaker 160 as well as the distribution line 158.

The electric power distribution system 100 may be monitored, controlled,automated, and/or protected using IEDs such as the IEDs 104, 106, 108,115, and 170, and an industrial control system 172. In general, the IEDsin an electric power generation and transmission system may be used forprotection, control, automation, and/or monitoring of equipment in thesystem. For example, the IEDs may be used to monitor equipment of manytypes, including electric transmission lines, electric distributionlines, current sensors, busses, switches, circuit breakers, reclosers,transformers, autotransformers, tap changers, voltage regulators,capacitor banks, generators, motors, pumps, compressors, valves, and avariety of other suitable types of monitored equipment.

As used herein, an IED (e.g., the IEDs 104, 106, 108, 115, and 170) mayrefer to any processing-based device that monitors, controls, automates,and/or protects monitored equipment within the electric powerdistribution system 100. Such devices may include, for example, remoteterminal units, differential relays, distance relays, directionalrelays, feeder relays, overcurrent relays, voltage regulator controls,voltage relays, breaker failure relays, generator relays, motor relays,automation controllers, bay controllers, meters, recloser controls,communications processors, computing platforms, programmable logiccontrollers (PLCs), programmable automation controllers, input andoutput modules, and the like. The term IED may be used to describe anindividual IED or a system including multiple IEDs. Moreover, an IED ofthis disclosure may use a non-transitory computer-readable medium (e.g.,memory) that may store instructions that, when executed by a processorof the IED, cause the processor to perform processes or methodsdisclosed herein. Moreover, the IED may include a wireless communicationsystem to receive and/or transmit wireless messages from a wirelesselectrical measurement device. The wireless communication system of theIED may be able to communicate with a wireless communication system ofthe wireless electrical measurement devices, and may include anysuitable communication circuitry for communication via a personal areanetwork (PAN), such as Bluetooth or ZigBee, a local area network (LAN)or wireless local area network (WLAN), such as an 802.11x Wi-Fi network,and/or a wide area network (WAN), (e.g., third-generation (3G) cellular,fourth-generation (4G) cellular, universal mobile telecommunicationsystem (UMTS), long term evolution (LTE), long term evolution licenseassisted access (LTE-LAA), fifth-generation (5G) cellular, and/or 5G NewRadio (5G NR) cellular).

A common time signal may be distributed throughout the electric powerdistribution system 100. Utilizing a common time source may ensure thatIEDs have a synchronized time signal that can be used to generate timesynchronized data, such as synchrophasors. In various embodiments, theIEDs 104, 106, 108, 115, and 170 may receive a common time signal 168.The time signal may be distributed in the electric power distributionsystem 100 using a communications network 162 and/or using a common timesource, such as a Global Navigation Satellite System (“GNSS”), or thelike.

According to various embodiments, the industrial control system 172 mayinclude one or more of a variety of types of systems. For example, theindustrial control system 172 may include a supervisory control and dataacquisition (SCADA) system and/or a wide area control and situationalawareness (WACSA) system. A central IED 170 may be in communication withIEDs 104, 106, 108, and 115 IEDs 104, 106, 108 and 115 may be remotefrom the central IED 170, and may communicate over various media such asa direct communication from IED 106 or over a communications network162. According to various embodiments, some IEDs may be in directcommunication with other IEDs. For example, the IED 104 may be in directcommunication with the central IED 170. Additionally or alternatively,some IEDs may be in communication via the communications network 162.For example, the IED 108 may be in communication with the central IED170 via the communications network 162.

Communication via the communications network 162 may be facilitated bynetworking devices including, but not limited to, multiplexers, routers,hubs, gateways, firewalls, and/or switches. In some embodiments, theIEDs and the network devices may include physically distinct devices. Incertain embodiments, the IEDs and/or the network devices may becomposite devices that may be configured in a variety of ways to performoverlapping functions. The IEDs and the network devices may includemulti-function hardware (e.g., processors, computer-readable storagemedia, communications interfaces, etc.) that may be utilized to performa variety of tasks that pertain to network communications and/or tooperation of equipment within the electric power distribution system100.

A communications controller 180 may interface with equipment in thecommunications network 162 to create a software-defined network (SDN)that facilitates communication between the IEDs 170, 115, and, 108 andthe industrial control system 172. In various embodiments, thecommunications controller 180 may interface with a control plane (notshown) in the communications network 162. Using the control plane, thecommunications controller 180 may direct the flow of data within thecommunications network 162.

The communications controller 180 may receive information from multipledevices in the communications network 162 regarding transmission ofdata. In embodiments in which the communications network 162 includesfiber optic communication links, the data collected by thecommunications controller 180 may include reflection characteristics,attenuation characteristics, signal-to-noise ratio characteristics,harmonic characteristics, packet loss statics, and the like. Inembodiments in which the communications network 162 includes electricalcommunication links, the data collected by the communications controller180 may include voltage measurements, signal-to-noise ratiocharacteristics, packet loss statics, and the like. In some embodiments,the communications network 162 may include both electrical and opticaltransmission media. The information collected by the communicationscontroller 180 may be used to assess a likelihood of a failure, togenerate information about precursors to a failure, and to identify aroot cause of a failure. The communications controller 180 may associateinformation regarding a status of various communication devices andcommunication links to assess a likelihood of a failure. Suchassociations may be utilized to generate information about theprecursors to a failure and/or to identify root cause(s) of a failureconsistent with embodiments of the present disclosure.

Some IEDs, such as the IED 108, may receive wireless messages from awireless electrical measurement device, such as the wireless currentsensor (WCS) 184. A wireless electrical measurement device such as thewireless current sensor (WCS) 184 may include a processor andnon-transitory computer-readable media that may store instructions that,when executed by the processor, cause the processor to obtain theelectrical measurements and transmit them wirelessly to an IED, such asthe IED 108. To that end, the wireless current sensor (WCS) 184 mayinclude a current transformer, a metering circuit, and a communicationsystem to wireless transmit measurements. The current transformer of thewireless current sensor (WCS) 184 may include a coil that may be loopedaround one phase of a distribution line (such as the distribution line158). The electrical current measurement of distribution line 158 may beobtained by measuring the electrical current induced in the coil of thecurrent transformer using the metering circuitry; the induced current isproportional to the current flowing through the measured phase of thedistribution line 158. In this way, the wireless current sensor (WCS)184 may measure an electrical current of an electrical waveform carriedby the distribution line 158. For example, the wireless current sensor(WCS) 184 may measure a current magnitude and a zero crossing of analternating current (AC) electrical waveform on the distribution line158. In some cases, there may be as many wireless current sensors (WCSs)184 as there are phases of electrical power on the distribution line158.

The wireless current sensor (WCS) 184 may send the electricalmeasurements as wireless messages to the IED 108 via an antenna 186. TheIED 108 may also use a time signal 168 to help the IED 108 assessarrival times of the wireless messages received by the IED 108 from thewireless current sensor (WCS) 184. The wireless messages may take anysuitable form and may be transmitted using any suitable protocol. Toconserve bandwidth, in some embodiments, the wireless messages maycontain a representation of the current magnitude measurement and may besent at a particular time based on a time of a zero crossingmeasurement. In one example, the wireless current sensor (WCS) 184 maytransmit a wireless message immediately upon a zero crossing, so thatthe IED 108 may identify the zero crossing based on the arrival time ofthe wireless message. In another example, the wireless current sensor(WCS) 184 may transmit a wireless message just prior to a zero crossing,so that the arrival time of the wireless message at the IED 108—takinginto account latencies of message transmission and receipt—is expectedto represent the present zero crossing of the electrical current carriedon the distribution line 158.

In some embodiments, the IED 108 may operate as a capacitor bankcontroller (CBC) that may control a capacitor bank (CB) 188. Thecapacitor bank (CB) 188 may represent an electrical component of thepower distribution system 100 that contains capacitors that can beselectively switched to connect to the distribution line 158. Becausethe capacitors of the capacitor bank (CB) 188 introduce a reactive loadto the distribution line 158 when connected to the distribution line158, the IED 108 may control the switching of the capacitors of thecapacitor bank (CB) 188 to control, for example, a power factor and/orphase shift on the distribution line 158. In addition to currentmeasurements from the wireless current sensor (WCS) 184, the IED 108 mayalso receive voltage measurements from a potential transformer 182.

FIG. 2 is an example three-phase voltage installation 200 with respectto the capacitor bank system 220 may include three capacitors 218A,218B, and 218C that correspond to three respective phases A, B, and C.The three capacitors 218A, 218B, and 218C may be coupled to threerespective switches 230A, 230B, and 230C. Further, the three respectivephases may be coupled to three respective fuses 236A, 236B, and 236C. Insome embodiments, there may be as many combo sensors as there are phasesof electrical power on the distribution line 246. For example, as shownby a three-phase arrangement in FIG. 2 , there may be three combosensors 224A, 224B, and 224C that measure voltage on three respectivephases A, B, and C carried by different conductors of the distributionline 246 (246A, 246B, and 246C). Current 248A, 248B, 248C (e.g., {rightarrow over (I_(CA))}, {right arrow over (I_(CB))}, {right arrow over(I_(CC))}) may be transmitted respectively across the distribution line246 (246A, 246B, and 246C). In some embodiments, the three combo sensor224A, 224B, and 224C may be three corresponding potential transformersthat obtain voltage measurements for the three respective phases A, B,and C.

The three-phase voltage installation 200 with respect to the capacitorbank system 220 may also include a neutral current sensor 202 that maymeasure the neutral current by measuring the electrical current on thethree respective phases A, B, and C. A control power transformer 208 maysupply voltage to the IED from either of the three respective phases A,B, and C and may be coupled to a junction box 206. The junction box 206may be a box containing a junction of electric wires or cables. Further,the junction box 206 may be coupled to the control power transformer208, three switch cables 216, and a junction box control cable 214. Thethree switch cables 216 may couple to the three respective switches230A, 230B, and 230C. The junction box control cable 214 may beconnected to a combined sensor connector 204. The combined sensorconnector 204 may have attributes of an intelligent electronic device(IED) or a capacitor bank controller (CBC) as described in FIG. 1 .Further, the combined sensor connector 204 may serve to connect to threesensor cables 210 and cables connecting to the neutral sensor 202. Thethree sensor cables 210 may couple to the three respective combo sensors224A, 224B, and 224C.

As mentioned above, failures within the three capacitors 218A, 218B, and218C, three respective switches 230A, 230B, and the three respectivefuses 236A, 236B, and 236C, may lead to open phase conditions within thethree-phase voltage installation 200 with respect to the capacitor banksystem 220. As such, different IED modes or operations (e.g., detectionmethods) may be effective to determine the number of open phases orfailures and which particular phase is open or has failed. In general, adetection method may involve calculating the fundamental frequency ofthe neutral current based on the electrical current at the threerespective phases A, B, and C. After determining the neutral current isgreater than a threshold current value, a power phasor for each rotationof the three-phase arrangement may be calculated. The IED may use themagnitude and angle of the power phasor to determine the presence ofopen phases, the number of open phases, and which particular phases maybe open. Detection methods may vary in how the power phasor is computedfor each rotation. The two different detection methods will be discussedin greater detail below.

As such, FIG. 3 is a flowchart of a process 250 by which particulardetection method identifies open phases by calculating a single phasorfor each rotation of a three-phase voltage installation. With respect tothis particular detection method, an IED (e.g., capacitor bankcontroller) may receive a neutral current measurement from a neutralcurrent sensor (block 252). As described above, the neutral current isthe sum of the electrical current of the three respective phases A, B,and C of the capacitor bank system. After receiving the neutral current,the IED may determine whether the magnitude of the neutral current(e.g., |{right arrow over (I_(N))}|) is greater than a first thresholdvalue (e.g., Th1) (block 254). If the magnitude of the calculatedneutral current is less than the first threshold value, then the IED maydetermine that each phase of the capacitor bank system is closed.However, if the magnitude of the calculated neutral current is greaterthan the first threshold value, then the IED may determine the presenceof open phases within the capacitor bank system. In turn, to determinethe number of open phases and which particular phases may be open, theIED may compute a power phasor for each rotation of the three-phasevoltage installation with respect to the capacitor bank system (block256).

The IED may use the three voltages (e.g., {right arrow over (V_(A))},{right arrow over (V_(B))}, {right arrow over (V_(C))}) obtained at therespective phases A, B, and C as well as the electrical current (e.g.,{right arrow over (I_(CA))}, {right arrow over (I_(CB))}, {right arrowover (I_(CC))}) based on the fundamental frequency of the neutralcurrent at the respective phases A, B, and C to calculate the powerphasor (e.g., {right arrow over (P_(ND))}) at each rotation. The powerphasor at a single phase is the vector product of the voltage at thesingle phase and the fundamental frequency of the neutral current. Inaccordance with the detection method of FIG. 3 , the power phasor ateach rotation may be calculated based on summing the vector product ofthe voltage at each phase A, B, and C of the three-phase voltageinstallation and the neutral current. Rotations of the three-phasevoltage installation may include an ABC rotation and an ACB rotation.The following power phasor formulas may be used to calculate the powerphasor for each rotation:

${{For}{ABC}\text{rotation:}}{\overset{arrow}{P_{ND}} = {{\overset{arrow}{V_{1}}*\overset{arrow}{I_{N}}} = {V_{A}I_{CA}\langle {90 + {V_{A}I_{CB}\langle {{- 30} + {V_{A}I_{CC}\langle {{- 150} + {V_{B}I_{CA}\langle {90 + \text{ }{V_{B}I_{CB}\langle {{- 30} + {V_{B}I_{CC}\langle {{- 150} + {V_{C}I_{CA}\langle {90 + {V_{C}I_{CB}\langle {{- 30} + {V_{C}I_{CC}\langle {- 150} }} }} }} }} }} }} }} }} }}}$${{For}{ACB}{rotation}}{\overset{arrow}{P_{ND}} = {{\overset{arrow}{V_{1}}*\overset{arrow}{I_{N}}} = {V_{A}I_{CA}\langle {90 + {V_{A}I_{CB}\langle {{- 150} + {V_{A}I_{CB}\langle {{- 300} + {V_{B}I_{CA}\langle {90 + \text{ }{V_{B}I_{CB}\langle {{- 150} + {V_{B}I_{CC}\langle {{- 30} + {V_{C}I_{CA}\langle {90 + {V_{C}I_{CB}\langle {{- 150} + {V_{C}I_{CC}\langle {- 30} }} }} }} }} }} }} }} }} }}}$

As mentioned above, the three-phase arrangement generally involves threealternating-current (AC) electrical waveforms that are offset from oneanother in phase by about 120°. As such, voltage and neutral currentmeasurements at the three phases going through the capacitor bank A, B,and C may correspond to the three angles 90°, −150°, and −30° dependingon an ABC or ACB rotation. After calculating the power phasor for eachrotation, the IED may determine whether the magnitude of the powerphasor is greater than a second threshold value (Th2) (block 258). Ifthe magnitudes of the power phasor is less than the second thresholdvalue, then the IED may determine that each phase of the capacitor banksystem may be closed even though the neutral current may have beengreater than the first threshold value. In other embodiments, the IEDmay notify maintenance personnel regarding the magnitudes the powerphasor being less than the second threshold value despite the neutralcurrent being greater than the first threshold value. The maintenancepersonnel may conduct further testing and/or analyze data received fromthe IED to verify whether each phase of the capacitor bank system isclosed.

However, if the magnitude of the power phasor is greater than the secondthreshold value, the IED may determine the presence of open phases inthe capacitor bank system. As discussed in the following figures, theIED may determine the number of open phases and which particular phasesmay be open based on the angle of the power phasor (block 260).

Further, the first threshold value and the second threshold value mayconfigurable. The first threshold value and the second threshold valuemay be empirical values set by the IED or manufacturer of the capacitorbank system 220. The first threshold value and the second thresholdvalue may be modified based on observing patterns and changes in valuesrelated to voltage and electrical current measurement for each phase,magnitude and angle corresponding to the power phasor of each rotation,and the like over time. In some embodiments, the first threshold valueand the second threshold value may be based on a nominal voltage andexpected capacitor bank size of a capacitor bank system. Afterdetermining which particular phases may be open, the IED may transmit anotification in real-time to computing device(s) monitored bymaintenance personnel or manufacturers of the capacitor bank systemregarding the open phases, such that the capacitor bank failuresassociated with the open phases may be addressed.

FIG. 4 is a schematic diagram representing an ABC rotation 300 of athree-phase arrangement of the capacitor bank system 220. The IED maydetermine which particular phases may be open based on the angle of thepower phasor (e.g., phase angle). According to the schematic diagram ofFIG. 4 , if the phase angle is between 0° and 60°, then the IED maydetermine that phase C is open, as indicated by angle range 302. If thephase angle is between 60° and 120°, then the IED may determine thatphases B and C is open, as indicated by angle range 304. If the phaseangle is between 120° and 180°, then the IED may determine that phase Bis open, as indicated by angle range 306. If the phase angle is between180° and 240°, then the IED may determine that phases A and B are open,as indicated by angle range 308. If the phase angle is between 240° and300°, then the IED may determine that phase A is open, as indicated byangle range 310. If the phase angle is between 300° and 360°, then theIED may determine that phases A and C are open, as indicated by anglerange 312. For example, with respect to the ABC rotation, if the phaseangle is −25° or 335°, then the IED may determine that phases A and Care open. In some embodiments, the angle ranges 302, 304, 306,308, 310,and 312 may be configurable.

FIG. 5 is a schematic diagram representing an ACB rotation 350 of athree-phase arrangement of the capacitor bank system 220. The IED maydetermine which particular phases may be open based on the angle of thepower phasor (e.g., phase angle). According to the schematic diagram ofFIG. 5 , if the phase angle is between 0° and 60°, then the IED maydetermine that phase B is open, as indicated by angle range 352. If thephase angle is between 60° and 120°, then the IED may determine thatphases B and C is open, as indicated by angle range 354. If the phaseangle is between 120° and 180°, then the IED may determine that phase Cis open, as indicated by angle range 356. If the phase angle is between180° and 240°, then the IED may determine that phases A and C are open,as indicated by angle range 358. If the phase angle is between 240° and300°, then the IED may determine that phase A is open, as indicated byangle range 360. If the phase angle is between 300° and 360°, then theIED may determine that phases A and B are open, as indicated by anglerange 362. For example, with respect to the ABC rotation, if the phaseangle is −25° or 335°, then the IED may determine that phases A and Bare open. In some embodiments, the angle ranges 352, 354, 356,358, 360,and 362 may be configurable.

With the foregoing in mind, FIG. 6 is a flowchart of a process 400 bywhich another detection method identifies open phases by calculatingthree power phasors corresponding to the respective phases A, B, and Cfor each rotation of a three-phase voltage installation. With respect tothis particular detection method, an IED (e.g., capacitor bankcontroller) may receive a neutral current measurement from a neutralcurrent sensor (block 402). As described above, the neutral current isthe sum of the electrical current of the three respective phases A, B,and C of the capacitor bank system. After receiving the neutral current,the IED may determine whether the magnitude of the neutral current(e.g., |{right arrow over (I_(N))}|) greater than a first thresholdvalue (e.g., Th1) (block 404). If the magnitude of the calculatedneutral current is less than the first threshold value, then the IED maydetermine that each phase of the capacitor bank system is closed.However, if the magnitude of the calculated neutral current is greaterthan the first threshold value, then the IED may determine the presenceof open phases within the capacitor bank system. In turn, to determinethe number of open phases and which particular phases may be open, theIED may compute three power phasors corresponding to the respectivephases A, B, and C for each rotation of the three-phase voltageinstallation with respect to the capacitor bank system (block 406).

The IED may use each of the three voltages (e.g., {right arrow over(V_(A))}, {right arrow over (V_(B))}, {right arrow over (V_(C))})obtained at the respective phases A, B, and C as well as each ofelectrical current (e.g., {right arrow over (I_(CA))}, {right arrow over(I_(CB))}, {right arrow over (I_(CC))}) based on the fundamentalfrequency of the neutral current at the respective phases A, B, and C tocalculate three different power phasors (e.g., {right arrow over(P_(NA))}, {right arrow over (P_(NB))}, {right arrow over (P_(NC))})corresponding to the respective phases A,B, and C at each rotation. Thepower phasor at a single phase (e.g., phase A) is the vector product ofthe voltage (e.g., V_(A)) at the single phase and the fundamentalfrequency of the neutral current (e.g, {right arrow over (I_(N))}).Rotations of the three-phase voltage installation may include an ABCrotation and an ACB rotation. The following power phasor formulas may beused to calculate the three power phasors for each rotation:

-   -   For ABC rotation:        {right arrow over (P _(NA))}={right arrow over (V _(A))}*{right        arrow over (I _(N))}=V _(A) I _(CA)        90+V _(A) I _(CB)        −30 +V _(A) I _(CC)        −150        {right arrow over (P _(NB))}={right arrow over (V _(B))}*{right        arrow over (I _(N))}=V _(B) I _(CA)        −30+V _(B) I _(CB)        −150+V _(B) I _(CC)        90        {right arrow over (P _(NC))}={right arrow over (V _(C))}*{right        arrow over (I _(N))}=V _(C) I _(CA)        −150+V _(C) I _(CB)        90+V _(C) I _(CC)        −30    -   For ACB rotation:        {right arrow over (P _(NA))}={right arrow over (V _(A))}*{right        arrow over (I _(N))}=V _(A) I _(XA)        90+V _(A) I _(CB)        −150+V _(A) I _(CC)        −30        {right arrow over (P _(NB))}={right arrow over (V _(B))}*{right        arrow over (I _(N))}=V _(B) I _(CA)        −150+V _(B) I _(CB)        −30+V _(B) I _(CC)        90        {right arrow over (P _(NC))}={right arrow over (V _(C))}*{right        arrow over (I _(N))}=V _(C) I _(CA)        −30+V _(C) I _(CB)        90+V _(C) I _(CC)        −150

As mentioned above, the three-phase arrangement generally involves threealternating-current (AC) electrical waveforms that are offset from oneanother in phase by about 120°. As such, voltage and neutral currentmeasurements at the three phases going through the capacitor bank A, B,and C may correspond to the three angles 90°, −150°, and −30° dependingon an ABC or ACB rotation. After calculating the three different powerphasors for each rotation, the IED may determine whether each of themagnitude of the three power phasor is greater than a third thresholdvalue (Th3) (block 408). If the magnitudes of each of the three powerphasors is less than the third threshold value, then the IED maydetermine that each phase of the capacitor bank system may be closedeven though the neutral current may have been greater than the firstthreshold value. In other embodiments, the IED may notify maintenancepersonnel regarding the magnitudes of each of the three power phasorsbeing less than the third threshold value despite the neutral currentbeing greater than the first threshold value. The maintenance personnelmay conduct further testing and/or analyze data received from the IED toverify whether each phase of the capacitor bank system is closed.

However, if the magnitudes of each of the three power phasors is greaterthan the third threshold value (e.g., |{right arrow over (P_(NA))}|>Th3,|{right arrow over (P_(NB))}|>Th3, |{right arrow over (P_(NC))}|>Th3),the IED may determine the presence of open phases in the capacitor banksystem. As discussed in the following figures, the IED may determine thenumber of open phases and which particular phases may be open based onthe angle of each of the three power phasors (block 410). It should benoted that the third threshold value may be different than the secondthreshold value of FIG. 3 and the first threshold value of FIGS. 3 and 6. In some embodiments, the third threshold value may be similar in valueto the second threshold value of FIG. 3 and the first threshold value ofFIGS. 3 and 6 .

Similar to the detection method of FIG. 3 , the first threshold valueand the third threshold value may configurable. That is, the firstthreshold value and the third threshold value may be empirical valuesset by the IED or manufacturer of the capacitor bank system 220. Thefirst threshold value and the third threshold value may be modifiedbased on observing patterns and changes in values related to voltage andelectrical current measurement for each phase, magnitude and anglecorresponding to the power phasor of each rotation, and the like overtime. In some embodiments, the first threshold value and the thirdthreshold value may be based on a nominal voltage and expected capacitorbank size of a capacitor bank system. After determining which particularphases may be open, the IED may transmit a notification in real-time tocomputing device(s) monitored by maintenance personnel or manufacturersof the capacitor bank system regarding the open phases, such that thecapacitor bank failures associated with the open phases may beaddressed.

FIG. 7 is a schematic diagram of an ABC rotation 450 used to identify asingle open phase based on each phase angle of the three different powerphasors calculated in FIG. 6 . The IED may determine which particularphase may be open based on the angle of each of the three power phasors(e.g., {right arrow over (P_(NA))}, {right arrow over (P_(NB))}, {rightarrow over (P_(NC))}). According to the schematic diagram of FIG. 7 , ifphase angle C is between 0° and 60° (as indicated by angle range 454),phase angle B is between 120° and 180° (as indicated by angle range456), phase angle A is between 240° and 300° (as indicated by anglerange 458), or any combination thereof, then the IED may determine thatphase A is open. The IED may determine that phase B is open if phaseangle B is between 0° and 60° (as indicated by angle range 462), phaseangle A is between 120° and 180° (as indicated by angle range 464),phase angle C is between 240° and 300° (as indicated by angle range466), or any combination thereof. Further, the IED may determine thatphase C is open if phase angle A is between 0° and 60° (as indicated byangle range 470), phase angle C is between 120° and 180° (as indicatedby angle range 472), phase angle B is between 240° and 300° (asindicated by angle range 474), or any combination thereof. For example,with respect to the ABC rotation, if the phase angle A is 30°, phaseangle B is 250°, and phase angle C is 160°, then the IED may determinethat phase C is open. In some embodiments, the angle ranges 454, 456,458, 462, 464, 466, 470, 472, and 474 may be configurable.

FIG. 8 is another schematic diagram of an ABC rotation 500 used toidentify at least two open phases based on each phase angle of the threedifferent power phasors calculated in FIG. 6 . The IED may determinewhich two particular phases may be open based on the angle of each ofthe three power phasors (e.g., {right arrow over (P_(NA))}, {right arrowover (P_(NB))}, {right arrow over (P_(NC))}). According to the schematicdiagram of FIG. 8 , if phase angle B is between 60° and 120° (asindicated by angle range 504), phase angle A is between 180° and 240°(as indicated by angle range 506), phase angle C is between 300° and360° (as indicated by angle range 508), or any combination thereof, thenthe IED may determine that phases A and B are open. The IED maydetermine that phases A and C are open if phase angle C is between 60°and 120° (as indicated by angle range 512), phase angle B is between180° and 240° (as indicated by angle range 514), phase angle A isbetween 300° and 360° (as indicated by angle range 516), or anycombination thereof. Further, the IED may determine that phases B and Care open if phase angle A is between 60° and 120° (as indicated by anglerange 520), phase angle C is between 180° and 240° (as indicated byangle range 522), phase angle B is between 300° and 360° (as indicatedby angle range 524), or any combination thereof. For example, withrespect to the ABC rotation, if the phase angle A is 80°, phase angle Bis 320°, and phase angle C is 200°, then the IED may determine thatphases B and C are open. In some embodiments, the angle ranges 504, 506,508, 512, 514, 516, 520, 522, and 524 may be configurable.

FIG. 9 is a schematic diagram of an ACB rotation 550 used to identify asingle open phase based on each phase angle of the three different powerphasors calculated in FIG. 6 . The IED may determine which particularphase may be open based on the angle of each of the three power phasors(e.g., {right arrow over (P_(NA))}, {right arrow over (P_(NB))}, {rightarrow over (P_(NC))}) According to the schematic diagram of FIG. 9 , ifphase angle C is between 0° and 60° (as indicated by angle range 552),phase angle B is between 120° and 180° (as indicated by angle range554), phase angle A is between 240° and 300° (as indicated by anglerange 556), or any combination thereof, then the IED may determine thatphase A is open. The IED may determine that phase B is open if phaseangle B is between 0° and 60° (as indicated by angle range 558), phaseangle A is between 120° and 180° (as indicated by angle range 560),phase angle C is between 240° and 300° (as indicated by angle range562), or any combination thereof. Further, the IED may determine thatphase C is open if phase angle A is between 0° and 60° (as indicated byangle range 564), phase angle C is between 120° and 180° (as indicatedby angle range 566), phase angle B is between 240° and 300° (asindicated by angle range 568), or any combination thereof. For example,with respect to the ABC rotation, if the phase angle A is 30°, phaseangle B is 250°, and phase angle C is 160°, then the IED may determinethat phase C is open. In some embodiments, the angle ranges 552, 554,556, 558, 560, 562, 564, 566, and 568 may be configurable.

FIG. 10 is another schematic diagram of an ACB rotation 600 used toidentify at least two open phases based on each phase angle of the threedifferent phasors calculated in FIG. 6 . The IED may determine which twoparticular phases may be open based on the angle of each of the threepower phasors (e.g., {right arrow over (P_(NA))}, {right arrow over(P_(NB))}, {right arrow over (P_(NC))}). According to the schematicdiagram of FIG. 10 , if phase angle B is between 60° and 120° (asindicated by angle range 602), phase angle C is between 180° and 240°(as indicated by angle range 604), phase angle A is between 300° and360° (as indicated by angle range 606), or any combination thereof, thenthe IED may determine that phases A and B are open. The IED maydetermine that phases A and C are open if phase angle C is between 60°and 120° (as indicated by angle range 608), phase angle A is between180° and 240° (as indicated by angle range 610), phase angle C isbetween 300° and 360° (as indicated by angle range 612), or anycombination thereof. Further, the IED may determine that phases B and Care open if phase angle A is between 60° and 120° (as indicated by anglerange 614), phase angle B is between 180° and 240° (as indicated byangle range 616), phase angle C is between 300° and 360° (as indicatedby angle range 618), or any combination thereof. For example, withrespect to the ABC rotation, if the phase angle A is 80°, phase angle Bis 200°, and phase angle C is 320°, then the IED may determine thatphases B and C are open. In some embodiments, the angle ranges 602, 604,606, 608, 610, 612, 614, and 618 may be configurable.

While specific embodiments and applications of the disclosure have beenillustrated and described, it is to be understood that the disclosure isnot limited to the precise configurations and components disclosedherein. For example, the systems and methods described herein may beapplied to an industrial electric power delivery system or an electricpower delivery system implemented in a boat or oil platform that may ormay not include long-distance transmission of high-voltage power.Accordingly, many changes may be made to the details of theabove-described embodiments without departing from the underlyingprinciples of this disclosure. The scope of the present disclosureshould, therefore, be determined only by the following claims.

Indeed, the embodiments set forth in the present disclosure may besusceptible to various modifications and alternative forms, specificembodiments have been shown by way of example in the drawings and havebeen described in detail herein. However, it may be understood that thedisclosure is not intended to be limited to the particular formsdisclosed. The disclosure is to cover all modifications, equivalents,and alternatives falling within the spirit and scope of the disclosureas defined by the following appended claims. In addition, the techniquespresented and claimed herein are referenced and applied to materialobjects and concrete examples of a practical nature that demonstrablyimprove the present technical field and, as such, are not abstract,intangible or purely theoretical. Further, if any claims appended to theend of this specification contain one or more elements designated as“means for [perform]ing [a function] . . . ” or “step for [perform]ing[a function] . . . ”, it is intended that such elements are to beinterpreted under 35 U.S.C. 112(f). For any claims containing elementsdesignated in any other manner, however, it is intended that suchelements are not to be interpreted under 35 U.S.C. 112(f).

What is claimed is:
 1. A method, comprising: determining a neutralcurrent of a multi-phase capacitor bank system based on a neutralcurrent sensor; in response to a magnitude of the neutral current beinggreater than a first threshold value, calculating a power phasor withrespect to an ABC rotation, an ACB rotation, or both of the multi-phasecapacitor bank system, wherein the power phasor comprises a vectorproduct of a voltage measured by a respective combo sensor at a phase ofone or more phases of the multi-phase capacitor bank system and afundamental frequency of the neutral current; in response to a magnitudeof the power phasor being greater than a second threshold value:determining, via an intelligent electronic device (IED), that the one ormore phases are open within the multi-phase capacitor bank system;determining, via the IED, which of the one or more phases are open basedon a phase angle of the power phasor; and transmitting, via the IED, anotification indicating the one or more phases that are open.
 2. Themethod of claim 1, wherein the first threshold value and the secondthreshold value are based on a nominal voltage and expected capacitorbank size of the multi-phase capacitor bank system.
 3. The method ofclaim 1, wherein the neutral current is determined based on a summationof electrical current associated with each phase of the multi-phasecapacitor bank system.
 4. The method of claim 1, comprising determiningthat a third phase is open with respect to the ABC rotation anddetermining a second phase is open with respect to the ACB rotation whenthe phase angle is between 0° and 60°.
 5. The method of claim 1,comprising determining that a second phase and a third phase are openwhen the phase angle is between 60° and 120° with respect to the ABCrotation and the ACB rotation.
 6. The method of claim 1, comprisingdetermining that a second phase is open with respect to the ABC rotationand determining that a third phase is open with respect to the ACBrotation when the phase angle is between 120° and 180°.
 7. The method ofclaim 1, comprising determining that a first phase and a second phaseare open with respect to the ABC rotation and determining the firstphase and a third phase are open with respect to the ACB rotation whenthe phase angle is between 180° and 240°.
 8. The method of claim 1,comprising determining that a first phase is open when the phase angleis between 240° and 300° with respect to the ABC rotation and the ACBrotation.
 9. The method of claim 1, comprising determining that a firstphase and a third phase are open with respect to the ABC rotation anddetermining that the first phase and a second phase are open withrespect to the ACB rotation when the phase angle is between 300° and360°.
 10. The method of claim 1, wherein the first threshold value, thesecond threshold value, or both, are based on a nominal voltage and abank size of the multi-phase capacitor bank.
 11. One or more tangible,non-transitory, computer-readable media comprising instructions that,when executed by a processor of an intelligent electronic deviceconfigured to control at least part of an electric power distributionsystem, cause the processor to: determine a neutral current of amulti-phase capacitor bank system based on a neutral current sensor; inresponse to a magnitude of the neutral current being greater than afirst threshold value, calculate a power phasor for each phase themulti-phase capacitor bank system with respect to an ABC phase rotation,an ACB phase rotation, or both, wherein the power phasor comprises avector product of a voltage measured by a respective combo sensor ateach phase of one or more phases of the multi-phase capacitor banksystem and a fundamental frequency of the neutral current; in responseto each magnitude of each power phasor being greater than a secondthreshold value, determine that the one or more phases are open withinthe multi-phase capacitor bank system and therefore: determine, via theintelligent electronic device (IED), which of the one or more phases areopen based on each phase angle of each power phasor; and transmit, viathe IED, a notification indicating the one or more phases that are open.12. The one or more tangible, non-transitory, computer-readable media ofclaim 11, comprising instructions that, when executed by the processor,cause the processor to determine that a first phase is open with respectto the ABC phase rotation and the ACB phase rotation when a phase angleof the first phase is between 240° and 300°, a phase angle of a secondphase is between 120° and 180°, and a phase angle of a third phase isbetween 0° and 60°.
 13. The one or more tangible, non-transitory,computer-readable media of claim 11, comprising instructions that, whenexecuted by the processor, cause the processor to determine that asecond phase is open with respect to the ABC phase rotation and the ACBphase rotation when a phase angle of a first phase is between 120° and180°, a phase angle of the second phase is between 0° and 60°, and aphase angle of a third phase is between 240° and 300°.
 14. The one ormore tangible, non-transitory, computer-readable media of claim 11,comprising instructions that, when executed by the processor, cause theprocessor to determine a third phase is open with respect to the ABCphase rotation and the ACB phase rotation when a phase angle of a firstphase is between 0° and 60°, a phase angle of a second phase is between240° and 300°, and a phase angle of a third phase is between 120° and180°.
 15. The one or more tangible, non-transitory, computer-readablemedia of claim 11, comprising instructions that, when executed by theprocessor, cause the processor to determine a first phase and a secondphase are open with respect to the ABC phase rotation when a phase angleof the first phase is between 180° and 240°, a phase angle of the secondphase is between 60° and 120°, and a phase angle of a third phase isbetween 300° and 360°.
 16. The one or more tangible, non-transitory,computer-readable media of claim 11, comprising instructions that, whenexecuted by the processor, cause the processor to determine that a firstphase and a third phase are open with respect to the ABC phase rotationwhen a phase angle of the first phase is between 300° and 360°, a phaseangle of a second phase is between 180° and 240°, and a phase angle ofthe third phase is between 60° and 120°.
 17. The one or more tangible,non-transitory, computer-readable media of claim 11, comprisinginstructions that, when executed by the processor, cause the processorto determine that a second phase and a third phase are open with respectto the ABC phase rotation when a phase angle of a first phase is between60° and 120°, a phase angle of the second phase is between 300° and360°, and a phase angle of the third phase is between 180° and 240°. 18.An intelligent electronic device, comprising: processing circuitry; acommunication system; and a memory device comprising instructions thatcause the processing circuitry to: calculate a power phasor for eachphase of a multi-phase capacitor bank system with respect to an ABCphase rotation, an ACB phase rotation, or both, wherein the power phasorcomprises a vector product of a voltage received from a respective combosensor at each phase of one or more phases of the multi-phase capacitorbank system and a fundamental frequency of a neutral current receivedfrom a neutral current sensor; in response to each magnitude of eachpower phasor being greater than a threshold value: determine which ofthe one or more phases are open based on each phase angle of each powerphasor; and issue a notification indicating the one or more phases thatare open.
 19. The intelligent electronic device of claim 18, wherein thethreshold value is configurable based at least in part on a nominalvoltage and expected capacitor bank size of the multi-phase capacitorbank system.
 20. The intelligent electronic device of claim 18,comprising determining a neutral current of the multi-phase capacitorbank system via a plurality of current sensors, wherein each currentsensor corresponds to a phase of the multi-phase capacitor bank system,and determining that the one or more phases are open within response todetermining that a magnitude of the neutral current is greater thananother threshold value.
 21. The intelligent electronic device of claim18, comprising instructions that cause the processing circuitry todetermine that a first phase and a second phase are open with respect tothe ACB phase rotation when a phase angle of the first phase is between300° and 360°, a phase angle of the second phase is between 60° and120°, and a phase angle of a third phase is between 180° and 240°. 22.The intelligent electronic device of claim 18, comprising instructionsthat cause the processing circuitry to determine that a first phase anda third phase are open with respect to the ACB phase rotation when aphase angle of the first phase is between 180° and 240°, a phase angleof a second phase is between 300° and 360°, and a phase angle of thethird phase is between 60° and 120°.
 23. The intelligent electronicdevice of claim 18, comprising instructions that cause the processingcircuitry to determine that a second phase and a third phase are openwith respect to the ACB phase rotation when a phase angle of a firstphase is between 60° and 120°, a phase angle of the second phase isbetween 180° and 240°, and a phase angle of the third phase is between300° and 360°.
 24. The intelligent electronic device of claim 18,wherein the multi-phase capacitor bank system comprises a three-phasecapacitor bank system.